LLVM 19.0.0git
ConstraintSystem.cpp
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1//===- ConstraintSytem.cpp - A system of linear constraints. ----*- C++ -*-===//
2//
3// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
4// See https://llvm.org/LICENSE.txt for license information.
5// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
6//
7//===----------------------------------------------------------------------===//
8
13#include "llvm/IR/Value.h"
14#include "llvm/Support/Debug.h"
15
16#include <string>
17
18using namespace llvm;
19
20#define DEBUG_TYPE "constraint-system"
21
22bool ConstraintSystem::eliminateUsingFM() {
23 // Implementation of Fourier–Motzkin elimination, with some tricks from the
24 // paper Pugh, William. "The Omega test: a fast and practical integer
25 // programming algorithm for dependence
26 // analysis."
27 // Supercomputing'91: Proceedings of the 1991 ACM/
28 // IEEE conference on Supercomputing. IEEE, 1991.
29 assert(!Constraints.empty() &&
30 "should only be called for non-empty constraint systems");
31
32 unsigned LastIdx = NumVariables - 1;
33
34 // First, either remove the variable in place if it is 0 or add the row to
35 // RemainingRows and remove it from the system.
36 SmallVector<SmallVector<Entry, 8>, 4> RemainingRows;
37 for (unsigned R1 = 0; R1 < Constraints.size();) {
38 SmallVector<Entry, 8> &Row1 = Constraints[R1];
39 if (getLastCoefficient(Row1, LastIdx) == 0) {
40 if (Row1.size() > 0 && Row1.back().Id == LastIdx)
41 Row1.pop_back();
42 R1++;
43 } else {
44 std::swap(Constraints[R1], Constraints.back());
45 RemainingRows.push_back(std::move(Constraints.back()));
46 Constraints.pop_back();
47 }
48 }
49
50 // Process rows where the variable is != 0.
51 unsigned NumRemainingConstraints = RemainingRows.size();
52 for (unsigned R1 = 0; R1 < NumRemainingConstraints; R1++) {
53 // FIXME do not use copy
54 for (unsigned R2 = R1 + 1; R2 < NumRemainingConstraints; R2++) {
55 if (R1 == R2)
56 continue;
57
58 int64_t UpperLast = getLastCoefficient(RemainingRows[R2], LastIdx);
59 int64_t LowerLast = getLastCoefficient(RemainingRows[R1], LastIdx);
60 assert(
61 UpperLast != 0 && LowerLast != 0 &&
62 "RemainingRows should only contain rows where the variable is != 0");
63
64 if ((LowerLast < 0 && UpperLast < 0) || (LowerLast > 0 && UpperLast > 0))
65 continue;
66
67 unsigned LowerR = R1;
68 unsigned UpperR = R2;
69 if (UpperLast < 0) {
70 std::swap(LowerR, UpperR);
71 std::swap(LowerLast, UpperLast);
72 }
73
75 unsigned IdxUpper = 0;
76 unsigned IdxLower = 0;
77 auto &LowerRow = RemainingRows[LowerR];
78 auto &UpperRow = RemainingRows[UpperR];
79 while (true) {
80 if (IdxUpper >= UpperRow.size() || IdxLower >= LowerRow.size())
81 break;
82 int64_t M1, M2, N;
83 int64_t UpperV = 0;
84 int64_t LowerV = 0;
85 uint16_t CurrentId = std::numeric_limits<uint16_t>::max();
86 if (IdxUpper < UpperRow.size()) {
87 CurrentId = std::min(UpperRow[IdxUpper].Id, CurrentId);
88 }
89 if (IdxLower < LowerRow.size()) {
90 CurrentId = std::min(LowerRow[IdxLower].Id, CurrentId);
91 }
92
93 if (IdxUpper < UpperRow.size() && UpperRow[IdxUpper].Id == CurrentId) {
94 UpperV = UpperRow[IdxUpper].Coefficient;
95 IdxUpper++;
96 }
97
98 if (MulOverflow(UpperV, -1 * LowerLast, M1))
99 return false;
100 if (IdxLower < LowerRow.size() && LowerRow[IdxLower].Id == CurrentId) {
101 LowerV = LowerRow[IdxLower].Coefficient;
102 IdxLower++;
103 }
104
105 if (MulOverflow(LowerV, UpperLast, M2))
106 return false;
107 if (AddOverflow(M1, M2, N))
108 return false;
109 if (N == 0)
110 continue;
111 NR.emplace_back(N, CurrentId);
112 }
113 if (NR.empty())
114 continue;
115 Constraints.push_back(std::move(NR));
116 // Give up if the new system gets too big.
117 if (Constraints.size() > 500)
118 return false;
119 }
120 }
121 NumVariables -= 1;
122
123 return true;
124}
125
126bool ConstraintSystem::mayHaveSolutionImpl() {
127 while (!Constraints.empty() && NumVariables > 1) {
128 if (!eliminateUsingFM())
129 return true;
130 }
131
132 if (Constraints.empty() || NumVariables > 1)
133 return true;
134
135 return all_of(Constraints, [](auto &R) {
136 if (R.empty())
137 return true;
138 if (R[0].Id == 0)
139 return R[0].Coefficient >= 0;
140 return true;
141 });
142}
143
144SmallVector<std::string> ConstraintSystem::getVarNamesList() const {
145 SmallVector<std::string> Names(Value2Index.size(), "");
146#ifndef NDEBUG
147 for (auto &[V, Index] : Value2Index) {
148 std::string OperandName;
149 if (V->getName().empty())
150 OperandName = V->getNameOrAsOperand();
151 else
152 OperandName = std::string("%") + V->getName().str();
153 Names[Index - 1] = OperandName;
154 }
155#endif
156 return Names;
157}
158
160#ifndef NDEBUG
161 if (Constraints.empty())
162 return;
163 SmallVector<std::string> Names = getVarNamesList();
164 for (const auto &Row : Constraints) {
166 for (unsigned I = 0, S = Row.size(); I < S; ++I) {
167 if (Row[I].Id >= NumVariables)
168 break;
169 if (Row[I].Id == 0)
170 continue;
171 std::string Coefficient;
172 if (Row[I].Coefficient != 1)
173 Coefficient = std::to_string(Row[I].Coefficient) + " * ";
174 Parts.push_back(Coefficient + Names[Row[I].Id - 1]);
175 }
176 // assert(!Parts.empty() && "need to have at least some parts");
177 int64_t ConstPart = 0;
178 if (Row[0].Id == 0)
179 ConstPart = Row[0].Coefficient;
180 LLVM_DEBUG(dbgs() << join(Parts, std::string(" + "))
181 << " <= " << std::to_string(ConstPart) << "\n");
182 }
183#endif
184}
185
187 LLVM_DEBUG(dbgs() << "---\n");
188 LLVM_DEBUG(dump());
189 bool HasSolution = mayHaveSolutionImpl();
190 LLVM_DEBUG(dbgs() << (HasSolution ? "sat" : "unsat") << "\n");
191 return HasSolution;
192}
193
195 // If all variable coefficients are 0, we have 'C >= 0'. If the constant is >=
196 // 0, R is always true, regardless of the system.
197 if (all_of(ArrayRef(R).drop_front(1), [](int64_t C) { return C == 0; }))
198 return R[0] >= 0;
199
200 // If there is no solution with the negation of R added to the system, the
201 // condition must hold based on the existing constraints.
203 if (R.empty())
204 return false;
205
206 auto NewSystem = *this;
207 NewSystem.addVariableRow(R);
208 return !NewSystem.mayHaveSolution();
209}
#define LLVM_DEBUG(X)
Definition: Debug.h:101
#define I(x, y, z)
Definition: MD5.cpp:58
#define R2(n)
if(VerifyEach)
assert(ImpDefSCC.getReg()==AMDGPU::SCC &&ImpDefSCC.isDef())
This file defines the SmallVector class.
This file contains some functions that are useful when dealing with strings.
ArrayRef - Represent a constant reference to an array (0 or more elements consecutively in memory),...
Definition: ArrayRef.h:41
static SmallVector< int64_t, 8 > negate(SmallVector< int64_t, 8 > R)
bool mayHaveSolution()
Returns true if there may be a solution for the constraints in the system.
bool isConditionImplied(SmallVector< int64_t, 8 > R) const
void dump() const
Print the constraints in the system.
unsigned size() const
Definition: DenseMap.h:99
bool empty() const
Definition: SmallVector.h:94
size_t size() const
Definition: SmallVector.h:91
reference emplace_back(ArgTypes &&... Args)
Definition: SmallVector.h:950
void push_back(const T &Elt)
Definition: SmallVector.h:426
This is a 'vector' (really, a variable-sized array), optimized for the case when the array is small.
Definition: SmallVector.h:1209
@ C
The default llvm calling convention, compatible with C.
Definition: CallingConv.h:34
This is an optimization pass for GlobalISel generic memory operations.
Definition: AddressRanges.h:18
std::enable_if_t< std::is_signed_v< T >, T > MulOverflow(T X, T Y, T &Result)
Multiply two signed integers, computing the two's complement truncated result, returning true if an o...
Definition: MathExtras.h:679
bool all_of(R &&range, UnaryPredicate P)
Provide wrappers to std::all_of which take ranges instead of having to pass begin/end explicitly.
Definition: STLExtras.h:1722
unsigned M1(unsigned Val)
Definition: VE.h:376
raw_ostream & dbgs()
dbgs() - This returns a reference to a raw_ostream for debugging messages.
Definition: Debug.cpp:163
std::enable_if_t< std::is_signed_v< T >, T > AddOverflow(T X, T Y, T &Result)
Add two signed integers, computing the two's complement truncated result, returning true if overflow ...
Definition: MathExtras.h:627
void swap(llvm::BitVector &LHS, llvm::BitVector &RHS)
Implement std::swap in terms of BitVector swap.
Definition: BitVector.h:860
#define N